Abstract

We examine the corporate governance roles of information quality and the takeover market with asymmetric information regarding the value of the target firm. Increasing information quality improves the takeover efficiency however, a highly efficient takeover market also discourages the manager from exerting effort. We find that perfect information quality is not optimal for either current shareholders’ expected payoff maximization or expected firm value maximization. Furthermore, current shareholders prefer a lower level of information quality than the level that maximizes expected firm value, because of a misalignment between current shareholders’ value and total firm value. We also analyze the impact of antitakeover laws, and find that the passage of antitakeover laws may induce current shareholders to choose a higher level of information quality and thus increase expected firm value.

From this equation, \(\phantom {\dot {i}\!}{\Pi }_{r}(p,\,\hat {h})\) decreases with p when \(\phantom {\dot {i}\!}p\geq p_{h}\) or \(\phantom {\dot {i}\!}p_{l}\leq p<p_{h}\). As a result, the optimal p that maximizes \(\phantom {\dot {i}\!}{\Pi }_{r}(p,\,\hat {h})\) will be either \(\phantom {\dot {i}\!}p_{h}\) or \(\phantom {\dot {i}\!}p_{l}\), while all other prices are dominated.

In the following, we solve for the equilibrium given the information quality d and the manager’s private benefit m. We need to check that for the bidding strategies as shown in Lemma 2, the manager’s optimal effort in response to the bidding strategies is consistent with the conjectures.

We can prove that given \(\phantom {\dot {i}\!}C2\), \(\phantom {\dot {i}\!}Prob(OT|e^{*},\,\alpha _{G}^{*},\,\alpha _{B}^{*})\) is concave and has a unique maximum point at \(\phantom {\dot {i}\!}d=\frac {2-m}{2-m+m\gamma v_{0}}\).

It is easy to show that \(\phantom {\dot {i}\!}{\Pi }_{v}\) is continuous in both d and m. We consider two cases separately: (i) when \(\phantom {\dot {i}\!}m\le \frac {1}{1+\gamma v_{0}}\), and (ii) when \(\phantom {\dot {i}\!}m>\frac {1}{1+\gamma v_{0}}\). In each case, the choice of information quality d also affects which equilibrium holds. Therefore, we need to compare the payoffs in each possible equilibrium and determine the optimal information quality for firm value.

Similar to the proof of Proposition 2, we consider all possible cases for the values of m, \(\phantom {\dot {i}\!}v_{0}\), and \(\phantom {\dot {i}\!}\gamma \). In each case, the choice of information quality d also affects which equilibrium holds. We need to compare the payoffs in each possible equilibrium and determine the optimal information quality for expected firm value. In each case that we consider below, if \(\phantom {\dot {i}\!}C1\) holds, then \(\phantom {\dot {i}\!}{\Pi }_{s}=m+(1-m)(1-\gamma )v_{0}\) for any information quality in this range. If \(\phantom {\dot {i}\!}C2\) holds, we then need to check whether the the unconstrained maximum point \(\phantom {\dot {i}\!}d_{s}\) is an interior solution.

Given the assumption \(\phantom {\dot {i}\!}m<v_{0}\), we can prove that \(\phantom {\dot {i}\!}v_{0}>\frac {1}{1+\gamma v_{0}}\) if and only if \(\phantom {\dot {i}\!}v_{0}>\frac {\sqrt {4\gamma + 1}-1}{2\gamma } \left (>\frac {1}{2}\right )\). Therefore we consider the following cases:

We have the same unconstrained maximum point \(\phantom {\dot {i}\!}d_{s}\) that maximizes \(\phantom {\dot {i}\!}{\Pi }_{s}\). By checking whether the interior solution exists for the optimization problem, we have:

Let \(\phantom {\dot {i}\!}\gamma \) and \(\phantom {\dot {i}\!}\gamma ^{\prime }\) be the acquirer’s shares of the synergy value before and after the adoption of anti-takeover laws, respectively, and \(\phantom {\dot {i}\!}0<\gamma ^{\prime }<\gamma <1\). We then consider how the adoption of antitakeover laws affects the conditions for each scenario to hold. If the scenario still holds, it is clear from the above results, that antitakeover laws then increase the optimal information quality. If the scenario does not hold, we need to find a new scenario and compare it with the old scenario.

If scenario 1 holds initially, then the optimal information quality after antitakeover laws either remains in the same range, or jumps to scenario 3 when \(\phantom {\dot {i}\!}\gamma \) decreases to \(\phantom {\dot {i}\!}\gamma ^{\prime }\). For example, suppose initially \(\phantom {\dot {i}\!}0<\gamma \leq 2-\sqrt {2}\), \(\phantom {\dot {i}\!}\frac {1}{2}<v_{0}\leq \frac {1}{2-\gamma }\), and \(\phantom {\dot {i}\!}m<v_{0}\) holds. If \(\phantom {\dot {i}\!}\gamma ^{\prime }\) is not too small such that \(\phantom {\dot {i}\!}\frac {1}{2}<v_{0}\leq \frac {1}{2-\gamma ^{\prime }}\) remains, then scenario 1 still holds with \(\phantom {\dot {i}\!}\gamma ^{\prime }\). If \(\phantom {\dot {i}\!}\gamma ^{\prime }\) is small enough such that \(\phantom {\dot {i}\!}\frac {1}{2-\gamma ^{\prime }}<v_{0}\), then scenario 1 does not hold, but scenario 3 holds. We can show a similar result for all of the conditions under scenario 1 and prove that \(\phantom {\dot {i}\!}d_{s}^{\ast \ast }\geq d_{s}^{\ast }\).

Proof

Proposition 5

We focus on the cases of A1 and A2, where condition C2 holds. In the proofs of Propositions 2 and 3, we have derived shareholder’s expected payoff and expected firm value given d and \(\phantom {\dot {i}\!}\gamma \) as

For simplicity, we assume after the antitakeover laws, the prevailing scenario does not change. If the scenario changes after the antitakeover laws, for example, if A1 holds with \(\phantom {\dot {i}\!}\gamma \) while A2 holds with \(\phantom {\dot {i}\!}\gamma ^{\prime }\) after the adoption of antitakeover laws, we can then consider it as a combination of A1 and A2, and show that our results remain.

Proof

Proposition 6

Under the generalized information system, and analogous to the equilibrium in the main setting, denoting \(\phantom {\dot {i}\!}h_{0}\equiv \frac {1}{1+\gamma v_{0}}\), we can derive the equilibrium as follows:

When the separating-price-bidding equilibrium sustains, we substitute \(\phantom {\dot {i}\!}\alpha _{G}^{*}= 1\), \(\phantom {\dot {i}\!}\alpha _{B}^{*}= 0\) and \(\phantom {\dot {i}\!}e^{*}=\frac {mL_{B}(L_{G}-1)}{L_{G}-L_{B}}\) into \(\phantom {\dot {i}\!}{\Pi }_{s}(L_{G},L_{B})\) and solve for the optimal \(\phantom {\dot {i}\!}L_{G}\) and \(\phantom {\dot {i}\!}L_{B}\). We find that the optimal level of likelihood ratios for current shareholders under the separating-price-bidding equilibrium is a corner solution: \(\phantom {\dot {i}\!}L_{Gs}=\frac {2-m}{m\gamma v_{0}}\) and \(\phantom {\dot {i}\!}L_{Bs}=\frac {L_{Gs}h_{0}}{h_{0}(1-m)+mL_{Gs}(2h_{0}+(1-h_{0})L_{Gs}-1)}\). Notice that this optimal corner solution in the separating-price-bidding equilibrium also approaches the conditions for the mixed-price-bidding equilibrium. Therefore, the separating-price-bidding equilibrium is weakly dominated by the mixed-price-bidding equilibrium. Similarly, we can also prove that the separating-price-bidding equilibrium is a dominated equilibrium for firm value maximization as well.

When the low-price-bidding equilibrium sustains, \(\phantom {\dot {i}\!}\alpha _{G}^{*}= 0\), \(\phantom {\dot {i}\!}\alpha _{B}^{*}= 0\) and \(\phantom {\dot {i}\!}e^{*}=m\). Both shareholder’s expected payoff and expected firm value are independent of the information system as long as the condition for sustaining the low-price-bidding equilibrium sustains \(\phantom {\dot {i}\!}L_{G}<\frac {h_{0}(1-m)}{m(1-h_{0})}\). We do not include this case in the proposition, but even with this case, in general we still have \(\phantom {\dot {i}\!}L_{Gs}^{*}\le L_{Gv}^{*}\).